"After Aegon and his dragons destroyed the combined armies of the Reach and the Rock at the Field of Fire, King Torrhen Stark bent the knee and swore fealty to the Targaryen Dynasty in order to spare the destruction of Winterfell...and his people. He was forever after known as "The King Who Knelt"."

After seeing Aegon's dragons and his massive host, Torrhen realized the war was already lost.

Instead of fighting he chose to bend the knee to spare his people and surrendered his crown. For his submission, Aegon named him Lord Paramount and Warden of the North. Robb Stark believes that Torrhen "saved thousands of lives that day."
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Torrhen bends the knee to Aegon and his sisters, foreverafter becoming known as the King Who Knelt.

In the A Song of Ice and Fire novels, Torrhen Stark's story is the same. It is believed he knelt at the place where the Inn of the Kneeling Man sits at the time of the books.

Torrhen's army numbered about 30,000 men, but the Targaryen army that came to meet him numbered about 45,000 - nor did this represent all of Aegon's new bannermen, just the ones directly facing him. Moreover, the Targaryens had their three huge dragons. Torrhen's bastard brother Brandon Snow volunteered to sneak into the Targaryen camp at night and attempt to kill all three dragons while they slept, but Torrhen judged that this was impossible and that the failed attempt would only invite further retaliation from the Targaryens, so he chose to surrender instead.

Torrhen Stark's decision to kneel before Aegon Targaryen saved the North from the devastation inflicted upon the Gardeners and the Lannisters. The Conqueror not only confirmed the Starks as the rulers of the North but he also allowed them to keep their own customs: the Targaryens' laws would rule over the North, but they could keep their local custom of personally beheaded condemned men instead of delegating the task to an executioner. Queen Rhaenys Targaryen, as part of her efforts to keep the realm together after the Conquest, organized a marriage between Lord Stark's daughter and Lord Arryn. However, although Torrhen had bent the knee, his sons did not want to serve the Targaryens. It was only over their strong protests that the marriage took place and they refused to attend the marriage. The North remained in the realm so it can be assumed that Torrhen was able to prevent his sons from rising up against the Targaryens. It is unknown if Torrhen was still alive when Aegon visited Winterfell in 33 AC, during his last royal progress.